Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data
Daghestan Electronic Mathematical Reports, Tome 1 (2014), pp. 56-70
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A symmetric tensor field in the Euclidian space of any dimension ${{\mathbb R}}^n$ can be reconstructed from its integrals along straight lines which form n-manifold. We obtained the new formulas reconstructing solenoidal part of the fields when a ray transform is known only on complex lines, intersecting a given curve, as well as a curve belonging to infinity. The new family of two-dimensional planes in ${{\mathbb R}}^n$ is introduced and the inversion formula is obtained for the case of differential forms of degree $2$ on the given integrals along the planes of this family.
Keywords:
symmetric tensor field, ray transform, reconstruction, complex of lines, solenoidal part, Radon transform of differential forms.
@article{DEMR_2014_1_a1,
author = {Z. G. Medzhidov},
title = {Handling ray transform of symmetric tensor fields and the {Radon} transform of differential forms on incomplete data},
journal = {Daghestan Electronic Mathematical Reports},
pages = {56--70},
publisher = {mathdoc},
volume = {1},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DEMR_2014_1_a1/}
}
TY - JOUR AU - Z. G. Medzhidov TI - Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data JO - Daghestan Electronic Mathematical Reports PY - 2014 SP - 56 EP - 70 VL - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DEMR_2014_1_a1/ LA - ru ID - DEMR_2014_1_a1 ER -
%0 Journal Article %A Z. G. Medzhidov %T Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data %J Daghestan Electronic Mathematical Reports %D 2014 %P 56-70 %V 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DEMR_2014_1_a1/ %G ru %F DEMR_2014_1_a1
Z. G. Medzhidov. Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data. Daghestan Electronic Mathematical Reports, Tome 1 (2014), pp. 56-70. http://geodesic.mathdoc.fr/item/DEMR_2014_1_a1/